The motivation behind ARCADE stems from a quiet crisis in hydrological monitoring. In many regions where water levels are continuously recorded, no properly defined rating curve exists, meaning that decades of stage records cannot be converted into discharge. That gap injects severe uncertainty into hydrological and hydrodynamic models, undermining flood forecasts, hydraulic structure design, and water availability studies, particularly for water-intensive activities such as irrigated agriculture. Traditional approaches fit a single power-law equation to the stage-discharge relationship, but rivers rarely cooperate with such simplicity. Alternative methods, including segmented rating curves, loop rating calibration under hysteresis, and period-restricted calibration, each carry narrow application scopes and often depend on user-imposed manual constraints, leading to excessive generalization when applied across diverse datasets.

Machine learning has been widely explored as a way out of this impasse, with artificial neural networks, fuzzy logic, symbolic regression, and support vector machines all demonstrating performance gains over conventional fitting. Yet these black-box models come with their own drawbacks: they offer little physical interpretability and typically require large training datasets that most existing streamgage cannot provide. ARCADE takes a different path, combining physically grounded rating curve methodologies with automated statistical diagnostics. The package runs through eight main procedures: data pre-processing, hydrological representativeness analysis, outlier detection, regime shift analysis, rating curve fitting, model validation, streamflow estimation, and final model evaluation. Together these steps form a pipeline that treats the gauging station not as a static equation but as a living hydraulic system whose behavior can change over time.

The technical heart of the software lies in its regime shift analysis. ARCADE stratifies daily stage data into three hydrological ranges using the 0.25 and 0.75 quantiles of the empirical distribution, separating low-flow, medium-flow, and high-flow conditions. It then applies the supLM Lagrange multiplier test from the R package strucchange to assess the stability of rating curve parameters over time. If the resulting p-value falls below 0.05, the stage-discharge relationship is deemed unstable, and the breakpoints function identifies statistically significant structural breaks. The series is segmented into hydraulic subgroups with precisely defined boundaries, each required to contain at least ten percent of total observations and a minimum of twelve records. If no break is confirmed, the software warns the user and keeps the series intact, preventing artificially induced segmentations that could distort the record.

Once subgroups are established, ARCADE fits rating curves using several complementary strategies. The traditional power-law approach begins by estimating h0, the stage at which discharge tends to zero, through either the Boiten method, one-dimensional optimization, or an automatic selection between the two. Fitting proceeds via linear regression on a logarithmic scale, with a retransformation correction derived from the residual variance to reduce bias when returning to the original units. For rivers where a single equation cannot capture the full range of behavior, the software performs piecewise fitting across hydraulic segments, iterating robust regressions that remove standardized residual outliers until convergence, and then verifying hydraulic continuity between adjacent segments so that estimated discharges do not jump artificially at transition points.

Perhaps the most sophisticated module addresses hysteresis, the phenomenon in which the same water level corresponds to different discharges depending on whether the river is rising or falling. ARCADE automatically classifies every observation as belonging to a rising, falling, or stable trend, then iteratively searches for the separation stage hsep above which the hysteresis loop opens. For each candidate value, independent curves are fitted to the middle segment and the two upper branches, and the hypothesis producing the smallest global residual sum of squares wins. The result is a looped rating curve that honors the pseudo-uniqueness of the stage-discharge relationship during flood waves, a condition common downstream of reservoirs and in reaches with variable backwater effects.

Validation is built into the workflow rather than left as an afterthought. Each hydraulic subgroup’s data are split into eighty percent calibration and twenty percent testing sets, with the test set selected to preserve representativeness across all hydrological ranges. Performance is quantified with the coefficient of determination, Nash-Sutcliffe efficiency, root mean square error, mean absolute error, mean absolute percentage error, and mean bias, while likelihood ratio tests statistically verify whether separate curves are genuinely distinct. In the illustrative examples, the software was applied to ten streamgage across Brazil, ranging from the 10.2-square-kilometer Mato Frio Creek catchment to the Solimões-Amazonas River at Óbidos, whose drainage area spans roughly 4.67 million square kilometers. Conditions included hysteresis at Itaqui on the Uruguay River, backwater effects at UHE Peti Carrapato, and temporal channel geometry changes on the Acre River.

The results were striking in many cases. At Floriano Peixoto, R-squared values on test data ranged from 0.981 to 0.997 across five fitted subgroups, with Nash-Sutcliffe efficiency between 0.942 and 0.997. At Rio Branco, R-squared and NSE remained near or above 0.98 for most fits. At UHE Peti Carrapato, a station considered highly unstable, ARCADE’s three-curve solution outperformed both official curves from Brazil’s National Water and Sanitation Agency and previously published annual fits. Comparisons with machine learning models at Óbidos, including XGBoost, decision trees, and random forests, showed that while those algorithms achieved high predictive scores, they offered no insight into the physical causes of changing hydraulic controls, whereas ARCADE integrates discharge estimation with an explicit investigation of the hydraulic conditions governing the stage-discharge relationship.

The software is not infallible, and its developers are candid about that. At Ponte Rio do Cachorro, test R-squared fell to 0.065 with negative NSE, a failure the diagnostics traced to instability in the section’s control conditions rather than to the fitting procedure itself, flagging the station for deeper hydraulic evaluation. The authors also caution that official rating curves evaluated without separating training and testing data can produce overly optimistic quality estimates, since using the same records for calibration and evaluation complicates the detection of overfitting. By enforcing an explicit split and honoring each equation’s validity interval, ARCADE offers a more honest assessment of generalization capacity, even when headline metrics look less flattering.

The broader implications extend well beyond academic hydrology. Because ARCADE runs on R 4.4.0 or later across Windows, macOS, and Linux, works with daily, sub-daily, and hourly records, and requires minimal manual intervention, it can serve as a decision-support tool for environmental monitoring agencies tasked with consolidating fragmented hydrometric archives. By systematically evaluating large datasets, diagnosing data quality, detecting regime shifts, and generating reproducible discharge series, the platform could help unlock decades of stranded stage records in regions where rating curves were never established. Its open-source availability under the MIT license invites researchers and practitioners everywhere to scrutinize, adapt, and extend the workflow, a transparency that proprietary hydrological software has rarely offered. For a field whose foundational data product, the river discharge record, depends on a curve fitted behind the scenes, bringing that process into rigorous, automated, and interpretable view may prove one of the more consequential software releases in water science this decade.

Subject of Research: Open-source software for automated river rating curve fitting and hydraulic diagnostics

Article Title: ARCADE: A software tool for advanced rating curve fitting, data evaluation and hydraulic diagnostics

Article References: dos Santos, L. A., Moreira, M. C., Dazilio, M. B., Amorim, R. S. S., & da Silva, D. D. (2026). ARCADE: A software tool for advanced rating curve fitting, data evaluation and hydraulic diagnostics. SoftwareX, 36, Article 103107. https://doi.org/10.1016/j.softx.2026.103107

Image Credits: AI Generated

DOI: Not provided

Keywords: ARCADE, rating curve, hydrology, river discharge, streamgage, hysteresis, stage-discharge relationship, open-source software, R programming, structural break detection, water resources management, hydraulic diagnostics